# Lesson 12

Connections between Graphs and Equations

- Let’s examine some situations, equations, and graphs.

### 12.1: Math Talk: Evaluating a Function

Here is a function: \(g(x)=100-5x\)

Evaluate mentally:

\(g(0)\)

\(g(1)\)

\(g(4)\)

\(g(20)\)

### 12.2: Bank Accounts

Each function represents the amount in a bank account after \(t\) weeks.

\(A(t) = 500\)

\(B(t) = 500 + 40t\)

\(C(t) = 500 - 40t\)

\(D(t) = 500 \boldcdot (1.5)^t\)

\(E(t) = 500 \boldcdot (0.75)^t\)

- Make a table for each bank account showing the money in the account at 0, 1, 2, and 3 weeks.
- Describe in words how the money in the account is changing week by week.
- Use technology to create a graph of each function. How can you see your description in each graph?

### 12.3: Build a New Function

Consider the same five functions:

\(A(t) = 500\)

\(B(t) = 500 + 40t\)

\(C(t) = 500 - 40t\)

\(D(t) = 500 \boldcdot (1.5)^t\)

\(E(t) = 500 \boldcdot (0.75)^t\)

- Starting with one of the functions, change it so that it represents an account that . . .
- Starts with a balance of $300, and loses $40 each week.
- Starts with a balance of $500, and gains $15 each week.
- Starts with a balance of $500, and loses \(\frac{1}{10}\) of its value each week.
- Starts with a balance of $700, and gains \(\frac{3}{10}\) of its value each week.

- Here are four graphs. Which graph matches each of your new equations?
- To check, use technology to graph your equations. Make sure to use the same graphing window. Check that the graph of your equation matches the graph you chose.